arXiv:2303.17633 · Physical review. B./Physical review. B

Interplay of many-body interactions and quasiperiodic disorder in the all-bands-flat diamond chain

Aamna Ahmed, Nilanjan Roy, Auditya Sharma

Published Jun 7, 2023• 5 citations

Abstract

We study the effects of quasiperiodic Aubry-Andr\'e (AA) disorder and interactions on a one-dimensional all-bands-flat (ABF) diamond chain. We consider the application of disorder in two ways: A symmetric one, where the same disorder is applied to the top and bottom sites of a unit cell, and an antisymmetric one, where the disorder applied to the top and bottom sites are of equal magnitude but with opposite signs. The single-particle wave-packet dynamics for the clean system and when the disorder is applied symmetrically show quantum caging; in the antisymmetric case, the wave packet spreads over the entire lattice. These results agree with our previous study, where compact localization was observed in the case of the clean system and for symmetrically disordered diamond lattices. In the presence of nearest-neighbor interactions, nonergodic phases are observed in the case of a clean system and symmetrical disorder; at higher disorder strengths, we find an MBL-like phase in the symmetric case. However, many-body nonequilibrium dynamics of the system from carefully engineered initial states exhibit quantum caging. In the antisymmetric case, a nonergodic mixed phase, a thermal phase, and an MBL-like phases, respectively, are observed at low, intermediate, and high disorder strengths. We observe an absence of caging and initial state dependence (except at the intermediate disorder strength) in the study of nonequilibrium dynamics.

DOI: 10.1103/physrevb.107.245110

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arXiv:2303.17633 · Physical review. B./Physical review. B

Interplay of many-body interactions and quasiperiodic disorder in the all-bands-flat diamond chain

Aamna Ahmed, Nilanjan Roy, Auditya Sharma

Published Jun 7, 2023• 5 citations

arXiv HTML PDF

Abstract

We study the effects of quasiperiodic Aubry-Andr'e (AA) disorder and interactions on a one-dimensional all-bands-flat (ABF) diamond chain. We consider the application of disorder in two ways: A symmetric one, where the same disorder is applied to the top and bottom sites of a unit cell, and an antisymmetric one, where the disorder applied to the top and bottom sites are of equal magnitude but with opposite signs. The single-particle wave-packet dynamics for the clean system and when the disorder is applied symmetrically show quantum caging; in the antisymmetric case, the wave packet spreads over the entire lattice. These results agree with our previous study, where compact localization was observed in the case of the clean system and for symmetrically disordered diamond lattices. In the presence of nearest-neighbor interactions, nonergodic phases are observed in the case of a clean system and symmetrical disorder; at higher disorder strengths, we find an MBL-like phase in the symmetric case. However, many-body nonequilibrium dynamics of the system from carefully engineered initial states exhibit quantum caging. In the antisymmetric case, a nonergodic mixed phase, a thermal phase, and an MBL-like phases, respectively, are observed at low, intermediate, and high disorder strengths. We observe an absence of caging and initial state dependence (except at the intermediate disorder strength) in the study of nonequilibrium dynamics.

DOI: 10.1103/physrevb.107.245110

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M

of participating particles in one- and higher-dimensional lattice---results that explain and generalize previous observations for two particles on a diamond chain [Vidal et al., Phys. Rev. Lett. 85, 3906 (2000)].

L=50

. We find that the choice of periodicity $\mathrm{\ensuremath{\Phi}}$ of the quasiperiodic field influences the dynamics. For $\mathrm{\ensuremath{\Phi}}=(\sqrt{5}\ensuremath{-}1)/2$ (the inverse golden ratio) and interaction $\mathrm{\ensuremath{\Delta}}=1$, the model most frequently considered in the literature, we obtain the critical disorder ${W}_{c}=4.8\ifmmode\pm\else\textpm\fi{}0.5$ in units where the noninteracting transition is at

W=2

. At the same time, for periodicity $\mathrm{\ensuremath{\Phi}}=\sqrt{2}/2$ we obtain a considerably higher critical value, ${W}_{c}=7.8\ifmmode\pm\else\textpm\fi{}0.5$. Finite-size effects on the critical disorder

{W}_{c}

are much weaker than in the purely random case. This supports the enhancement of

{W}_{c}

in the case of a purely random potential by rare ``ergodic spots,'' which do not occur in the quasiperiodic case. Further, the data suggest that the decay of the antiferromagnetic order in the delocalized phase is faster than a power law.

We study many-body localization (MBL) in the quasiperiodic ${t}_{1}\text{\ensuremath{-}}{t}_{2}$ model, focusing on the role of next-nearest-neighbor (NNN) hopping

{t}_{2}

, which introduces a single-particle mobility edge. The calculated phase diagram can be divided into three distinct regimes, depending on the strength of the short-range interaction

U

. For weak interactions ($U\ensuremath{\ll}{t}_{1}$), this model is always nonthermal. For intermediate interactions ($U\ensuremath{\sim}{t}_{1}$), the thermal-MBL phase transition in this model is qualitatively the same as that of the Aubry-Andre (AA) model, which is consistent with existing experimental observations. For strong interactions $(U\ensuremath{\gg}{t}_{1})$, the NNN hopping produces qualitatively new physics because it breaks down the Hilbert space fragmentation present in the AA model. The NNN hopping is thus irrelevant when the interaction is intermediate but relevant for strong interactions.